yesbird wrote:

> >> Since you have MatLab:
> >>
> >>
https://www.researchgate.net/publication/318476279_Algorithm_976_Bertini_real_Numerical_Decomposition_of_Real_Alge
braic
> >>
_Curves_and_Surfaces/download?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ
> >>
> >>
https://www.researchgate.net/publication/4278665_Interactive_Ray_Tracing_of_Arbitrary_Implicits_with_SIMD_Interval
_Arit
> >>
hmetic/download?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ
> >>
> >> Bezier patches and Bernstein polynomials!  :)
> >> https://cad-conference.net/files/CAD24/CAD24_334-338.pdf
>
> Yes, I have, but MathView is based on WebGL, has no relation to
> ray tracing, but in general this stuff is interesting.
> --
> YB

Well, what I was suggesting, is that since you wanted to use parametric
equations, maybe you could find a way to parameterize things like the Barth
Sextic.

That's all.   :)

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yesbird wrote:

>
> Yes, my latest project - online editor for math surfaces and curves
> assumes equations in parametric forms. MathView now in stable beta stage
> and ready to be filled with a content, I am already have a large list
> of candidates to this collection, fortunately they are free :).
>

Have a look at: http://3d-meier.de/tut3/Seite0.html
Lots of parametric equations but it is in German - not the equations :))
I used a whole bunch of them together with meshmaker.inc

Should you need help let me know.

> https://mathview.yesbird.online/

Nice work!

>
> Although it's not completed yet, I will be glad to get any kind of
> response, including suggestions, criticism and new ideas.
>
Just have a look at the screenshot.

Regards
Droj

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Attachments:
Download 'mathview.png' (3066 KB)

Preview of image 'mathview.png'

On 03/04/2025 21:22, Droj wrote:
> Have a look at: http://3d-meier.de/tut3/Seite0.html
> Lots of parametric equations but it is in German - not the equations :))
> I used a whole bunch of them together with meshmaker.inc
> 
> Should you need help let me know.

Oooo - this is a real royal gift !
Many thanks - this is the end of my quest, now I can concentrate on 
further development.

> 
>> https://mathview.yesbird.online/
> 
> Nice work!
> ... 
> Just have a look at the screenshot.
> 

Some things still need to be implemented, especially in XR mode.
Feedback you sent is very important - what resolution do you have ?
Design assumes 1920x1080, but maybe I should do something with this.
-- 
YB

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yesbird wrote:
>
> Oooo - this is a real royal gift !
> Many thanks - this is the end of my quest, now I can concentrate on
> further development.

You are more than welcome.

>
> Some things still need to be implemented, especially in XR mode.
> Feedback you sent is very important - what resolution do you have ?
> Design assumes 1920x1080, but maybe I should do something with this.
> --
> YB

Resolution is 1360x768
I use an old LG TV as monitor.

Droj

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On 4/3/25 11:37, Bald Eagle wrote:
> When I was making my tori last night, I was trying to capture that pinkish color
> that you have there.
> 
> Of course that's the part you snipped out . . .
> 
> What's the special sauce?

The trick was, at least partly, there in my post:

...
union {
     ...
     texture{
         pigment{ color rgb<1,1,1>}
         finish { emission <0.1,0,0> phong 0.5}  // <--- Here, emission
     }
     ...
}

However, you must also run with a v3.8 or later(*) release and set the 
version to 3.8 with a #version directive or ini / command line flag like 
+mv3.8.

V3.8 is needed because, with it, the default finish{}'s ambient value is 
always zero.

A better answer requires more, if I get back to that work, the detail 
should be in its own thread. For now, see the asides below.

(*) Lying. Radiosity sets ambient to zero in earlier versions - and 
users could always set it to zero.

---

Aside 1: Relatively late in the overall v3.8 development cycle, the 
ambient default value was changed from <0.1,0.1,0.1> to <0,0,0>, mostly 
based on the argument v3.7 and v3.8 renders of old scenes looked washed 
out due the gamma handling changes. These changes made the old ambient 
grey far too strong - because it wasn't, itself, gamma adjusted.

For me, the best reason for the v3.8 ambient <0,0,0> default, over - for 
example - a new srgb-space, gamma corrected one, is that any non-zero, 
grey value has always worked against per feature color support in 
POV-Ray.

---

Aside 2: With respect to quality renders, I believe we under-utilize the 
per feature / aspect, color functionality already in POV-Ray(*). 
Further, that with 'minor-ish' modifications, expanded, per feature, 
color functionality can be added /exploited.

(*) We often use single values for 3D color vector specifications. Or we 
think of and treat density{} as a single value proposition, when it's 
effectively a pigment{}.

Some years ago ('povr named fork' days), I merged existing, but 
variously named and, sometimes, mostly forgotten color control 
capabilities in POV-Ray under a single new 'amplify' color multiplier 
keyword. I went on to extended 'amplify' to additional features in 
today's yuqk fork.

Going to stop here. I find - and oddly enjoy - that so much with our 
POV-Ray play requires books to describe well! :-)

Bill P.

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William F Pokorny <ano### [at] anonymousorg> wrote:

>      texture{
>          pigment{ color rgb<1,1,1>}
>          finish { emission <0.1,0,0> phong 0.5}  // <--- Here, emission
>      }

Ah.  I'll have to play with that method a bit.
When I get home, I usually have all manner of things to attend to (or neglect ;)
) and I don't have the energy/creativity level to fully conceive of
experimenting in certain ways.

I also had some difficulty getting the rich, saturated colors that they show in
Fig 10:
https://www.sciencedirect.com/science/article/pii/S0898122114005252#f000030

I tried using the normal map method developed here:

https://news.povray.org/povray.binaries.images/message/%3Cweb.5da7f3c944e99bc863814b380%40news.povray.org%3E/#%3Cweb.5d
a7f3c944e99bc863814b380%40news.povray.org%3E

But everything was pretty washed out.

They might be using a completely different method / pattern for their coloring
function - which is interesting in itself.

- BW

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Hopefully you've also discovered:

http://xahlee.info/

?

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On 04/04/2025 16:32, Bald Eagle wrote:
> Hopefully you've also discovered:
> 
> http://xahlee.info/
> 
> ?
> 
Thanks, but comparing to:
https://virtualmathmuseum.org/

it's second-hand )
-- 
YB

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yesbird wrote:

> > http://xahlee.info/
> >
> > ?
> >
> Thanks, but comparing to:
> https://virtualmathmuseum.org/
>
> it's second-hand )
> --
> YB

Yes, second hand is right.

Take a look at:

https://www.frassek.org/

Might give some inspiration and offers parametric equations, too.

Droj

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On 05/04/2025 15:33, Droj wrote:
> Take a look at:
> 
> https://www.frassek.org/
> 
> Might give some inspiration and offers parametric equations, too.
> 
> Droj
> 

Many thanks, Droj !

This is really valuable information for me.
I will explore it more deeply, but right now I am enjoying these
two different approaches to shells modelling:
https://www.frassek.org/3d-mathe/meeresschnecken-muscheln/

Also I like accurate and beautiful design as well-thinked
organization of the site in general.

It's very pleasant to work with such resources.
--
YB

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